Speed after gliding with friction force present using work/E

In summary, the equation W= ΔKE = 1/2 mvf2-1/2 mvi2 was used to find the ice skater's speed after gliding 100m in a wind from the northeast. The initial velocity was 4.0m/s and a force of 4N was exerted on the skater. After solving for the final velocity using the given values, the correct answer was found to be 2.2m/s. It was determined that the skater would go slower due to the wind from the northeast.
  • #1
miyayeah
27
0

Homework Statement


The question is as follows: A 50kg ice skater is gliding along the ice, heading due north at 4.0m/s. The ice has a small coefficient of static friction, to prevent the skater from slipping sideways, but kinetic friction =0. Suddenly, a wind from the northeast exerts a force of 4N on the skater. Use work and energy to find the skater's speed after gliding 100m in this wind.

Homework Equations


W= F ⋅ d
W= ΔKE = 1/2 mvf2-1/2 mvi2

The Attempt at a Solution


W= F ⋅ d = (sin45)(4N)(100m) = 282.842712 J
In this step I assumed the angle to be 45 degrees because we are trying to find the y component of the force. (Since there is no movement sideways and speed is not affected by the sideway movement)
I used the above value of work in the next step. I rearranged the formula below to get final velocity.

W= ΔKE = 1/2 mvf2-1/2 mvi2
vf= √[(2W+mvi2)/m]

Plugging in the values from the question gave me 5.2 m/s. The correct answer was 2.2m/s.

Any help would be much appreciated!
 
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  • #2
Have a look at your last equation. If you add W and the initial kinetic energy, the final velocity must be larger than the initial one.
 
  • #3
miyayeah said:
heading due north

miyayeah said:
a wind from the northeast
So will the skater go faster or slower?
 
  • #4
haruspex said:
So will the skater go faster or slower?
Oh I read the question wrong. Thank you, I got the right answer this time.
 

Related to Speed after gliding with friction force present using work/E

1. How does friction affect an object's speed after gliding?

Friction is a force that opposes the motion of an object. This means that when an object is gliding, friction will act in the opposite direction of its motion, slowing it down. Therefore, the presence of friction will decrease the speed of an object after gliding.

2. What is the relationship between work and speed after gliding with friction force present?

The work done on an object is equal to the change in its kinetic energy. In the case of gliding with friction, the work done by the friction force will decrease the object's kinetic energy, resulting in a decrease in its speed. Therefore, there is an inverse relationship between work and speed after gliding with friction force present.

3. Can the speed after gliding with friction force present be greater than the initial speed?

No, the speed after gliding with friction force present cannot be greater than the initial speed. This is because the friction force will always act in the opposite direction of the object's motion, causing it to slow down. The object's initial speed is the maximum speed it can achieve in the absence of any external forces.

4. How can the work done by friction be calculated in this scenario?

The work done by friction can be calculated by multiplying the magnitude of the friction force by the distance the object travels while being acted upon by the friction force. This is represented by the equation W = Fd, where W is the work done, F is the friction force, and d is the distance traveled.

5. Does the mass of the object affect its speed after gliding with friction force present?

Yes, the mass of the object does affect its speed after gliding with friction force present. Objects with a larger mass will experience a greater friction force, resulting in a larger decrease in their speed. This is because the friction force is directly proportional to the mass of the object.

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